Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×M16×D53 | C2 | semidirect |
| 3. C2×#13133193 | C2 | semidirect |
| 4. #16810878 | C2 | semidirect |
| 5. #16810866 | C2 | semidirect |
| 6. #16810861 | C2 | semidirect |
| 7. #16810849 | C2 | semidirect |
| 8. #16810665 | C2 | semidirect |
| 9. #16810632 | C2 | semidirect |
| 10. #16810624 | C2 | semidirect |
| 11. C2×#137×C53 | C2 | semidirect |
| 33. #13133151 | C22 | semidirect |
| 34. #13133149 | C22 | semidirect |
| 35. #13133141 | C22 | semidirect |
| 36. #13133141 | C22 | semidirect |
| 37. #13133141 | C22 | semidirect |
| 38. #13133138 | C22 | semidirect |
| 42. C2×Q16×C53 | C22 | semidirect |
| 43. C2×SD16×C53 | C22 | semidirect |
| 70. M16×C53 | D4 | semidirect |
| 145. C2×D53 | #137 | semidirect |
| 164. C2×#137 | D53 | semidirect |
| 175. C53 | #3056 | semidirect |
| 180. C2×Q16 | C2×D53 | semidirect |
| 181. C2×SD16 | C2×D53 | semidirect |
| 236. M16 | C22⋊D53 | semidirect |